[Statistics] 4d6DL Point Buy Equivalent

[Thikket]

Someone sparked my interest in this, and as I could not find a thread dealing with such a comparison already, I decided to do one myself. Perhaps someone out there can benefit from this as well.

I wanted to see what the 4d6-drop-lowest method of rolling characters resulted in with regard to the point buy scale. So I wrote a MATLAB simulation function and ran it for 100,000 trials.

How many sets will you generate?100000
>>
The results are:
Number of valids: 87161
Number of rerolls: 12839
Average: 30.4445
Standard deviation: 7.89909

The average is about where I'd expect it to be (~30 point buy), but look at that standard deviation! That's exactly why I prefer point buy games. I don't want someone in my group to have a 22-point-buy equivalent character when the other guy over there has a 38-point-buy equivalent!

Here's the MATLAB code for my fellow dorks out there. I think it's pretty efficient.

% This program was created to calculate the point buy value of the 4d6 drop
% lowest rolling method.
%
% Rerolls: If the sum of the modifiers is 0 or lower, or if the highest
% ability score is 13 or lower.

function FourDSix


numCharacters=input('How many sets will you generate?');
counter=0;
numRerolls=0;
avg=0;
stddev=0;
base=[ 3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18];
mod=[-5 -4 -3 -2 -1  0  1  2  3  4  5  6  8 10 13 16];

for lcv=1:numCharacters
    % Generate the stats
    for mcv=1:6
        roll=[ceil(rand*6) ceil(rand*6) ceil(rand*6) ceil(rand*6)];
        [value1 index1] = max(roll);
        roll(index1)=0;
        [value2 index2] = max(roll);
        roll(index2)=0;
        [value3 index3] = max(roll);
        stat(mcv)=value1+value2+value3;
    end
    % Check for rerolls; if not needed, calculate point buy
    if max(stat)<14 || sum(floor((stat-10)/2))<1
        numRerolls=numRerolls+1;
    else
        counter=counter+1;
        % This stat changes into that point buy equivalent:
        %[ 3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18]
        %[-5 -4 -3 -2 -1  0  1  2  3  4  5  6  8 10 13 16]
        for ncv=1:6
            point(ncv)=mod(stat(ncv)==base);
        end
        data(counter)=sum(point);
    end
end

avg=mean(data);
stddev=std(data);
fprintf('The results are:\n Number of valids: %g\n Number of rerolls: %g\n Average: %g\n Standard deviation: %g\n',counter,numRerolls,avg,stddev);

Ahh, so good to post again... OH WAIT! I'm supposed to be a true lurker (it's a template)!

See you never!
Thikket

 

[Thanee]

There was a thread about it not too long ago, but the result was about the same.

Bye
Thanee

 

[Caeleddin]

There is a reason why NWN is a 30 point buy.


I find the 30pb to be too restrictive. Players will tend to mini/max. Also, it makes certain characters almost impossible to play. A Paladin will have a hard time competing with an Int/Cha 18 Wiz/Sorc. Spellcasters need to concentrate on 1 or, at most, 2 stats. Compare that with the fighter-types' mandatory 2 if not 3 or 4 stats.

That is why I like to give 4d6dl + a bit of pb (usually 1d10), skewed towards the low end (+1 cost for getting scores above 10). This is to encourage players to try and get rid of negatives instead of making their positives uber.

 

[FreeTheSlaves]

I thought the classes were balanced with the number of good scores needed in mind. There is no issues with our 25pt buy campaign characters, and two of them are the stat intensive monk & paladin.

 

[Shin Okada]

My play group has been using 32 point buy since the release of 3.0e. While it is true that most spellcasters (especially wizards and sorcerers) tend to have key ability of 16-18, arcane casters need not only the key ability for their spells but need high con, and should better have above average dex (though not as important as con).

I have never heard of complaint from players of Paladins. It seems that most core classes are balanced very well with 32 point buy. Maybe except for monks.

 

[Thanee]

I find the 30pb to be too restrictive. Players will tend to mini/max. Also, it makes certain characters almost impossible to play.

You. Must. Get. Rid. Of. That. Earlier. Edition. Mindset. That. You. Need. Several. 18s. To. Be. Decent.



I have 28 PB characters with no stat higher than 14 or 15. Works fine.

Bye
Thanee

 

[Caeleddin]

*I* work fine with 30pb. I usually play the Sorceror-type anyway. No skin off my nose. It's watching a bunch of high stat, high stat, high stat, 8, 8, 8 PCs that hacks me off about pb.

 

[Shin Okada]

*I* work fine with 30pb. I usually play the Sorceror-type anyway. No skin off my nose. It's watching a bunch of high stat, high stat, high stat, 8, 8, 8 PCs that hacks me off about pb.

Three 8s? I often see characters with two 8s but rarely see someone with three 8s. 3 abilities modify saves. In addition to this, fighter types and arcane casters need at least 1 other key ability. In case of bards, clerics, druids, monks & rogues, they need multiple above average stats anyway. I don't say a character with three 8s is not a vaiable option (say, a wizard with str 8, dex 8 and cha 8). But I don't see such characters often.

 

[Caeleddin]

You don't. I do.....


Wizards with Cha, Wis and Str 8.
Fighters with Dex, Cha and Int 8.
Rogues with Cha, Str and Int 8.

Take your pick.

 

[yennico]

I run my campaigns with 28 pb. I dislike PCs having an 18 in an attribute without a minor weakness. 18 in an attribute is six points above an average attribute.